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Simplifying 0 = -16x2 + 8x + 30 Reorder the terms: 0 = 30 + 8x + -16x2 Solving 0 = 30 + 8x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -30 = -30 -30 + -8x + 16x2 = 30 + 8x + -16x2 + -30 + -8x + 16x2 Reorder the terms: -30 + -8x + 16x2 = 30 + -30 + 8x + -8x + -16x2 + 16x2 Combine like terms: 30 + -30 = 0 -30 + -8x + 16x2 = 0 + 8x + -8x + -16x2 + 16x2 -30 + -8x + 16x2 = 8x + -8x + -16x2 + 16x2 Combine like terms: 8x + -8x = 0 -30 + -8x + 16x2 = 0 + -16x2 + 16x2 -30 + -8x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -30 + -8x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -4x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -4x + 8x2)' equal to zero and attempt to solve: Simplifying -15 + -4x + 8x2 = 0 Solving -15 + -4x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + -0.5x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -0.5x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -0.5x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -0.5x + x2 = 0 + 1.875 -0.5x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -0.5x + x2 = 1.875 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 1.875 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1.875 + 0.0625 Combine like terms: 1.875 + 0.0625 = 1.9375 0.0625 + -0.5x + x2 = 1.9375 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1.9375 Calculate the square root of the right side: 1.391941091 Break this problem into two subproblems by setting (x + -0.25) equal to 1.391941091 and -1.391941091.Subproblem 1
x + -0.25 = 1.391941091 Simplifying x + -0.25 = 1.391941091 Reorder the terms: -0.25 + x = 1.391941091 Solving -0.25 + x = 1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.391941091 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.391941091 + 0.25 x = 1.391941091 + 0.25 Combine like terms: 1.391941091 + 0.25 = 1.641941091 x = 1.641941091 Simplifying x = 1.641941091Subproblem 2
x + -0.25 = -1.391941091 Simplifying x + -0.25 = -1.391941091 Reorder the terms: -0.25 + x = -1.391941091 Solving -0.25 + x = -1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.391941091 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.391941091 + 0.25 x = -1.391941091 + 0.25 Combine like terms: -1.391941091 + 0.25 = -1.141941091 x = -1.141941091 Simplifying x = -1.141941091Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.641941091, -1.141941091}Solution
x = {1.641941091, -1.141941091}
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